Use Euler's method with step size
0.1
\displaystyle {0.1}
0.1
to estimate
y
(
0.5
)
\displaystyle {y}{\left({0.5}\right)}
y
(
0.5
)
, where
y
(
x
)
\displaystyle {y}{\left({x}\right)}
y
(
x
)
is the solution of the initial-value problem
y
′
=
3
x
+
y
2
,
y
(
0
)
=
−
1.
\displaystyle {y}'={3}{x}+{y}^{{2}},\ \ \ {y}{\left({0}\right)}=-{1}.
y
′
=
3
x
+
y
2
,
y
(
0
)
=
−
1
.
y
(
0.5
)
=
\displaystyle {y}{\left({0.5}\right)}=
y
(
0.5
)
=
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